A traffic light of mass m = 18 kg hangs from a massless joint at point P
PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
A traffic light of mass m = 18 kg hangs from a massless joint at point P. Two ideal cables support point P: one cable is horizontal and is fastened to a building on the left; the second cable is attached to a building on the right and rises upward making an angle of 40° above the horizontal. The assembly remains at rest.
(a) Draw the free-body diagram for the point P, labeling each force clearly.
(b) Derive algebraic expressions for the magnitudes of the tensions T_h (horizontal cable) and T_s (slanted cable) in terms of the given angle, mass m, and physical constants.
(c) Calculate numerical values for T_h and T_s.
(d) If the slanted cable can withstand a maximum tension of 350 N before failing, determine the greatest mass that the traffic light can have while the system remains in static equilibrium.